The Stellar Kinematics in Our Milky Way Hai-Jun Tian, CTGU/MPIA Collaborators: Chao Liu, Hans-Walter Rix, etc.

Outline

Bulk motions: Evidences Negative Positive VR VR VR Z(kpc) Z(kpc) VZ Vz Vz R(kpc) Azimuthal angle R(kpc) williams et al. 2013 Carlin et al. 2013 8kpc Siebert et al. 2011; Widrow et al. 2012; Bovy et al. 2015; Sun et al. 2015

Bulk motions: explanations Siebert et al. 2012 bulk motions in Vr: VR (1) Perturbation by arms (siebert+ 2012; Feure+2014); (2) Perturbation by bar(Grand+2015); (3) Ellipticity(Kuijken & Tremaine 1994; rix & zaritsky 1995) 2d density wave bulk motions in Vz: (1) Miner merging(Gomez+2013); (2) Stellar warp(Drimmel+2000; López-Corredoira+2014) Which mechanisms are true? Perturbation from the spiral structure

SOLAR NEIGHBOORHOOD: SAMPLE SELECTION FG- stars with high temperature(blue points): K- stars with low temperature(red points): Additional criteria for all the FGK-stars: Dividing method: - 100<|z|<500, slicing 3 slices, overlapping 100pc each other - teff from 4000K to 7000K, dicing 6 bins - Finally, 209316 FGK stars (18 subsamples) left in total

SOLAR NEIGHBOORHOOD: METHOD velocity projection ellipsoid projection Construct the Likelihood: There are 9 free parameters: we can obtain the best fit values by maximizing the likelihood.

Results of LAMOST FGK The real LAMOST sample, and calibrated by mock

The age–Teff relation (to explain the non-zero net motions) analysis The age–Teff relation (to explain the non-zero net motions) The abrupt change in age is perfectly consistent with our sudden change in the velocity dispersions. Why: exist net asymmetric motion in all three orientations when Teff>6000! (Young).

OUTER DISK: SAMPLE SELECTION young old old RC age from Martig et al.2016 2 Gyr young RC 2 Age(Gyr) Young and old RCs are selected from 120 K RC candidates (Wan et al. 2015): |Z| < 1kpc; 7<R/kpc<14 Old RCs ( > 2 Gyr): 40K Young RCs ( < 2 Gyr): 20 K

OUTER DISK: Radial & Azimuthal Velocity in R<9.0kpc, both VR are negative; 0 km/s at R~9.0kpc; R>9.0kpc, vr~4-8km/s VR are different (up to 3km/s). U-shape Vphi the young population rotates faster than the old by 5 km/s.

Age Variation in Warp: Vertical Velocity Warp mechanism: dynamical torques (Shen+2006); misaligned infalling gas (Roskar+2010) (Liu, Tian + 2016, submitted to Nature)

GPS1 Proper Motion Catalog: DATA GAIA (1-year, <2mas) PS1 (>4 years, ~10mas) SDSS (~10 years ago, ~25 mas) 2MASS (~10 years ago, ~100 mas) It is difficult to cross-calibrate sources in the different surveys

GPS1 Proper Motion Catalog: result GPS(\alpha): 1.35 mas/yr GP(\alpha): 1.41 mas/yr GPS(\delta): 1.21 mas/yr GP(\delta): 1.23 mas/yr

GPS1 Proper Motion Catalog: result PS1(\alpha): 2.55 mas/yr PD(\alpha): 1.91 mas/yr PD(\delta): 1.71 mas/yr PS1(\delta): 2.12 mas/yr

Conclusions: Taking-Home points -- Bulk motions: - Young stars (Teff>6000K) takes the born informations. (Tian + 2015) - VR can be explained by Ellipticity of the disk induced by the rotating bar. (Tian + 2017) - Vz can be explained by stellar warp, we favor the misaligned infalling gas warp mechanism. (Liu, Tian + 2016) -- We derive the solar motion of (U⊙, V⊙, W⊙)=(9.58, 10.52, 7.01) km/s with respect to the local standard of rest. (Tian + 2015); The pattern speed of the bar is measured as 45 km/s/kpc. (Tian + 2017) -- We construct a proper motion catalog (GPS1): ~350M stars across 3/4 sky region, down to mr<20; The systematic error <0.3 mas/yr (~10x better than PPMXL, UCAC4), the precision ~1.5 mas/yr. (~4x better). - GPS2 after Gaia DR2

thanks

Validation of the Method

Results of the LAMOST sample The Solar motion with respect to the LSR The stars cooler than 6000K over all |z| bins are averagely old. Since they do not show significant gradient in <V> it is safe to assume that they are in equilibrium. Eq.(4.228) of Binney&Tremaine(2008) set h_R = 2.5; L~2*h_R=5.0 (kruit 1988)

Validation of the Method Validation with GCS data We selected a sub-sample of 3712 from the GCS dwarf stars with the criteria (5500K< Teff <6000K, U<200km/s, V<400km/s, and W<200km/s)

OUTER DISK (METHOD) observed los Velocity in gsr modeled los Velocity in GSR Construct the Likelihood: There are 3 free parameters: we can obtain the best fit values by maximizing the likelihood.